So we get 16 - 9 = 7 in the units column and 9 tens becomes 2 tens in the first row.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & & & & &7 \\ \hline \end{array}

For the tens place: 8 - 2 = 6.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & & & &6 &7 \\ \hline \end{array}

For the hundreds place: 3 - 1 = 2.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & & &2 &6 &7 \\ \hline \end{array}

For the thousands place: 6 - 0 = 6.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & &6 &2 &6 &7 \\ \hline \end{array}

So 6396 - 129 = 6267.

Idea summary

We can use a vertical algorithm to add and subtract numbers.

Money and change

How can we work out how much change we need to receive, when we buy something? Let's see some strategies to help.

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Examples

Example 2

When out shopping Luigi buys some groceries for \$17.70 and pays with a \$20 note.

Which of the following could be the change he gets?

An image of a 2 dollar coin and 2 20 cents coins.

An image of a 1 dollar coin, 2 50 cent coins, a 20 cent coin and a 10 cent coin.

Worked Solution

Create a strategy

Count up from the cost to the amount given. Use this table of values to help you.

A table showing the value of 2 dollar, 1 dollar, 50 cent, 20 cent, 10 cent and 5 cent coins.

Apply the idea

To find the change we can count up from \$17.70 to \$20.

We would need to count up by another 30 cents to get to \$18. Then if we count up by 2 we get to 20.

\displaystyle \text{Change}	\displaystyle =	\displaystyle 30\text{ cents} + \$2	Add the amounts we counted up by
	\displaystyle =	\displaystyle \$2.30	Add the values

For option A, we have two 20 cents coins which make 40 cents and a \$1 coin. If we add them we would get:

\displaystyle 40 \text{ cents} + \$1

\displaystyle =

\displaystyle \$1.40

Add the values

For option B, we have two 50 cents coins which make \$1, a 20 cent coin, a 10 cent coin, and a \$1 coin. If we add them we would get:

\displaystyle 20 \text{ cents} + 10\text{ cents} + \$1 +\$1

\displaystyle =

\displaystyle \$2.30

Add the values

This is equal to the change we found earlier so the answer is Option B.

Idea summary

To find change we can either:

Subtract the price from the amount paid.
Count up from the price to the amount paid.

Bank accounts

How does a bank statement work? Let's find out in this video.

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Examples

Example 3

A withdrawal is:

money taken out of a bank.

the amout of money in a bank account at any time.

money put into a bank account.

Worked Solution

Create a strategy

A withdrawal decreases your bank balance.

Apply the idea

A withdrawal is money taken out of a bank, option A.

Idea summary

A deposit is when we put money into our bank account.

A withdrawal is when we take money out of our bank account.

Budgets and saving

In this video we work out if we have budgeted enough for the end of year party.

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Examples

Example 4

Here is Sarah’s weekly budget.

Complete the table below:

Income		Expenses
\text{Wages}	\$80.00	\text{Phone}	\$7.50
\text{Umpiring}	\$35.00	\text{Bus ticket}	\$15.00
		\text{Entertainment}	\$24.60
		\text{Food}	\$43.35
\text{Total}	\$ ⬚	\text{Total}	\$90.45

Worked Solution

Create a strategy

Add up the values in the income column to get the total.

Apply the idea

Use a vertical algorithm. \begin{array}{c} & & &8 &0 &. &0 &0 \\ &+ & &3 &5 &. &0 &0 \\ \hline \\ \hline \end{array}

Add the numbers down each column starting from the hundredths column, then the tenths, units and tens column to get: \begin{array}{c} & & &8 &0 &. &0 &0 \\ &+ & &3 &5 &. &0 &0 \\ \hline & &1 &1 &5 &. &0 &0\\ \hline \end{array}

So the total income is \$115.00.

Income		Expenses
\text{Wages}	\$80.00	\text{Phone}	\$7.50
\text{Umpiring}	\$35.00	\text{Bus ticket}	\$15.00
		\text{Entertainment}	\$24.60
		\text{Food}	\$43.35
\text{Total}	\$ 115.00	\text{Total}	\$90.45

Sarah saves any money that she has not spent. How much does Sarah save each week?

Worked Solution

Create a strategy

Find the difference between the total income and the total expenses.

Apply the idea

Write in a vertical algorithm. \begin{array}{c} & &1 &1 &5 &. &0 &0 \\ &- & &9 &0 &. &4 &5 \\ \hline \\ \hline \end{array}

Begin with the hundredths column. We can see that 0 is less than 5, so we need to trade 1 tenth from the tenths place. But we have 0 tenth. So we need to trade 1 unit from the units place.

So we get 10 - 5 = 5 in the hundredths column and 0 tenths becomes 9 tenths and 5 units becomess 4 units in the first row.\begin{array}{c} & &1 &1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & & & & & &5 \\ \hline \end{array}

For the tenths place: 9 - 4 = 5.\begin{array}{c} & &1 &1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & & & & &5 &5 \\ \hline \end{array}

For the units place: 4 - 0 = 4.\begin{array}{c} & &1 &1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & & &4 &. &5 &5 \\ \hline \end{array}

For the tens column, we can see that 1 is less than 9, so we need to trade 1 hundred from the hundreds place.

So we get 11 - 9 = 2 in the tens column and 1 hundred becomes 0 hundreds.\begin{array}{c} & &0 &\text{}^1 1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & &2 &4 &. &5 &5 \\ \hline \end{array}

So Sarah saves \$24.55 each week.

Idea summary

When we need to work to a budget, we need to make sure our expenses (money we spend) are not more than our income (money we receive).

Outcomes

AC9M5N09

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation

5.08 Budgets

Ideas

Are you ready?

Examples

Example 1

Money and change

Examples

Example 2

Bank accounts

Examples

Example 3

Budgets and saving

Examples

Example 4

Outcomes

AC9M5N09

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